RREF

Output the RREF of the given matrix.

RREF (Reduced Row Echelon Form) is a matrix with the following properties.

• Every row whose entries are all $0$ (a zero row) is below every row that is not (a row with a nonzero entry).
• The leading coefficient of every nonzero row is $1$.
• The leading coefficient of every nonzero row is to the right of the leading coefficient of the row above it.
• In the column of the leading coefficient of every nonzero row, all other entries are $0$.

The first line gives $N$ and $M$, the dimensions of the matrix. ($1 \leq N, M \leq 5$)

The next $N$ lines each contain $M$ rational numbers. Each rational number is given as a fraction $P$/$Q$ in lowest terms. ($P \in \mathbb{Z} \cap \left[-9, 9\right]$, $Q \in \mathbb{Z} \cap \left(0, 9\right]$)

If $Q = 1$, only $P$ is given, and if $P > 0$, the sign is omitted.

Output the RREF of the given matrix.

Print each entry as a fraction $P$/$Q$ in lowest terms. If $Q = 1$, print only $P$, and if $P > 0$, omit the sign.

RREF stands for Reduced Row Echelon Form.